It doesn't seem sufficient, and would probably lead to age verification laws anyway.
Say you're a parent, with child, living in country A where someone becomes an adult when they're 18. Once the child is 18, they'll use their own devices/browsers/whatever, and the flag is no longer set. But before that, the flag is set.
Now in country B or in country C it doesn't matter that the age of becoming an adult is 15 and 30. Because the flag is set locally on the clients device, all they need to do is block requests with the flag, and assume it's faithful. Then other parents in country B or country C set/unset the flag on their devices when it's appropriate.
No need to tell actual ages, and a way for services to say "this is not for children", and parents are still responsible for their own children. Sounds actually pretty OK to me.
> should
I don't know if "should" is intended as a moral statement or a regulatory statement, but it's not at all unusual for server operators to need to comply with laws in the country in which they are operating…